Abstract
Modulating the frequency of a harmonic oscillator at nearly twice its natural frequency leads to amplification and self-oscillation. Above the oscillation threshold, the field settles into a coherent oscillating state with a well-defined phase of either $0$ or $\pi$. We demonstrate a quantum parametric oscillator operating at microwave frequencies and drive it into oscillating states containing only a few photons. The small number of photons present in the system and the coherent nature of the nonlinearity prevents the environment from learning the randomly chosen phase of the oscillator. This allows the system to oscillate briefly in a quantum superposition of both phases at once - effectively generating a nonclassical Schr\"{o}dinger's cat state. We characterize the dynamics and states of the system by analyzing the output field emitted by the oscillator and implementing quantum state tomography suited for nonlinear resonators. By demonstrating a quantum parametric oscillator and the requisite techniques for characterizing its quantum state, we set the groundwork for new schemes of quantum and classical information processing and extend the reach of these ubiquitous devices deep into the quantum regime.
Highlights
Parametric amplifiers and oscillators are quintessential devices used to amplify small electromagnetic signals [1,2,3], convert radiation from one frequency to another [4,5], create squeezed light and entangled photons [6,7], and realize new information processing architectures [8,9,10,11,12]
The power spectral density (PSD) of this signal, which we call “transient PSD” to distinguish it from the PSD measured at a steady state, contains multiple peaks evenly spaced by χ [Fig. 2(b)] due to the nonlinear energy-level structure
We measure the transient PSDs for coherent states ρ0 1⁄4 jαihαj, which we prepare by driving the system resonantly at ωc with 1-ns pulses of different amplitudes
Summary
Parametric amplifiers and oscillators are quintessential devices used to amplify small electromagnetic signals [1,2,3], convert radiation from one frequency to another [4,5], create squeezed light and entangled photons [6,7], and realize new information processing architectures [8,9,10,11,12] They operate by modulating a parameter, the natural frequency of the resonant circuit ωc, at approximately twice its frequency ωp ≈ 2ωc (Fig. 1). A sufficiently large amplification overtakes the detuning and decay present in the system and leads to an exponential increase in the halfharmonic cavity field amplitude Nonlinearities clamp this exponential growth and cause the system to enter an oscillating steady state (Fig. 1). A†a†aaˆ þβðtÞða þ a†2Þ; ð1Þ where βðtÞ is the slowly varying amplitude of the parametric driving
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